Equations of Circles
Name: ________________________________
1
1. A circle is referred to as a conic section. What is meant by this?
2. What is the definition of a circle?
3. Derive the general equation of a circle if it has a center at C(h,k) with a
radius of r.
P(x,y)
(y - k)
C(h,k)
4. Determine the center and radius of the given circles.
2
2
a)  x  7    y  10   81
Center (_____ , _____)
Radius = _______
b) 100   x  3  y 2
Center (_____ , _____)
Radius = _______
c)  x  9    y  2   1
Center (_____ , _____)
Radius = _______
Center (_____ , _____)
Radius = _______
Center (_____ , _____)
Radius = _______
Center (_____ , _____)
Radius = _______
2
2
2
d) 36   x  8    y  7 
2
2
e) x 2   y  1  4
2
f) 0   x  1   y  11  9
2
2
5. Determine the equation of the circle.
a)
b)
(x - h)
c)
B
A
A
B
B
A
Equation of Circle A:
___________________________
Equation of Circle B:
___________________________
Equation of Circle A:
___________________________
Equation of Circle B:
___________________________
Equation of Circle A:
___________________________
Equation of Circle B:
___________________________
G.GPE.A.1 WORKSHEET #1 – PATTERSON
d)
2
e)
f)
B
A
A
A
B
B
Equation of Circle A:
___________________________
Equation of Circle A:
___________________________
Equation of Circle A:
___________________________
Equation of Circle B:
___________________________
Equation of Circle B:
___________________________
Equation of Circle B:
___________________________
6. Determine the equation of circle C.
a) Radius = 7 cm
C (-3,6)
b) Radius = 1 cm
C (5,-1)
c) Radius = 2.5 cm
C (0,-3)
____________________________
____________________________
____________________________
d) Radius = 10 cm
e) Radius = 2 cm
f) Radius = 14 cm
C (3,-3)
____________________________
C (-8,0)
____________________________
____________________________
7. Graph the following.
2
2
a)  x  3   y  2   4
c) x 2   y  5   25
b)  x  6    y  7   9
d)  x  4    y  7   9
2
2
2
2
C (-9,1)
2